Some discretisations of geophysical fluids include a step in which the vector transport equation is solved in isolation.
One such discretisation is the shallow-water model of [1]} and [2]}, which uses a compatible finite element framework.
This section briefly describes this model, which is used for the demonstrations in Section , applied to the lowest-order finite element spaces that correspond to those used by the Met Office's LFRic model [3]}, so that the velocity field \(\mathbf {u}\)  and the depth field \(h\)  are in the \(\mathrm {RTc}^f_1\)  and \(\mathrm {DG}_0\)  spaces respectively.
